We compute the bispectrum of the 2dF Galaxy Redshift Survey (2dFGRS) and use it to measure the bias parameter of the galaxies. This parameter quantifies the strength of clustering of the galaxies relative to the mass in the Universe. By analysing 80 × 106 triangle configurations in the wavenumber range 0.1 < k < 0.5 h Mpc-1 (i.e. on scales roughly between 5 and 30 h-1 Mpc) we find that the linear bias parameter is consistent with unity: b1 = 1.04 ± 0.11, and the quadratic (non-linear) bias is consistent with zero: b2 = -0.054 ± 0.08. Thus, at least on large scales, optically selected galaxies do indeed trace the underlying mass distribution. The bias parameter can be combined with the 2dFGRS measurement of the redshift distortion parameter β ≃ Ω0.6m/b1, to yield Ωm = 0.27 ± 0.06 for the matter density of the Universe, a result that is determined entirely from this survey, independent of other data sets. Our measurement of the matter density of the Universe should be interpreted as Ωm at the effective redshift of the survey (z = 0.17).